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Free Fall Motion

  1. Aug 30, 2004 #1
    A ball is thrown horizontally from a height of 15.75 m and hits the ground with a speed that is 5.0 times its initial speed. What was the initial speed?


    I thought you might have to find time and I got t=1.79s, but after that I cannot seem find my way to the answer

    Thanks to whom ever can help me out,

    Eleet
    Shaun
     
  2. jcsd
  3. Aug 30, 2004 #2

    Doc Al

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    The fact that the ball is thrown horizontally tells you that the vertical (y) component of the initial velocity is zero. So the initial velocity is purely x-component. Find the vertical component of the final velocity considering that the ball falls the given distance. (Hint: use a kinematic equation relating speed and distance for accelerated motion.)
     
  4. Aug 30, 2004 #3
    ??

    I do not know if this right but I found:
    Vf=17.58m/s
    by using Vf^2=2ad.

    Than how do I use this to find initial velocity horizontally. Or is that it?
     
  5. Aug 30, 2004 #4
    the initial velocity will be what ever it is, this same velocity is also part of the final.

    so [itex] \Vec {V_f}: [V_x,V_y] = 5\Vec {V_i}: [V_x,0] [/itex]
     
    Last edited: Aug 30, 2004
  6. Aug 30, 2004 #5

    Tide

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    Be careful! That's 5 times the speed - not velocity! :-)
     
  7. Aug 30, 2004 #6
    right, but the initial speed is a velocity with only one component, namely the x
    But I did put them in the wrong order
     
  8. Aug 30, 2004 #7

    Tide

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    More to the point: [tex]v_x^2+v_y^2 = 25 v_x^2[/tex]
     
  9. Aug 31, 2004 #8

    Doc Al

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    What you found is the y-component of the final velocity. Good! The final velocity has two components: [itex]v_x[/itex] (which is just the initial speed) and [itex]v_y[/itex] (which you just found).

    Now apply what was given in the problem statement: that the final speed is 5 times the initial speed. Tide gives you the formula:
    Note that the initial speed is [itex]v_x[/itex], which is what you're trying to find.

    Do you understand how Tide got his formula?
     
  10. Aug 31, 2004 #9
    undefinedundefinedI got it. :biggrin:

    we know height so we need to use this formula:

    (5Vo)^2=Vo^2+ g2h
    >>> Subtract out the Vo^2
    >>>>24Vo^2=2gh
    >>>>>Vo^2=2gh /2

    then, Vo=3.6m/s :laughing:
     
    Last edited: Aug 31, 2004
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